Klein Bottle Logophysics, Self-reference, Heterarchies, Genomic Topologies, Harmonics and Evolution. Part I: Morphomechanics, Space and Time in Biology & Physics, Cognition, Non-Linearity and the Stru

We discuss the contextual information associated with the Klein Bottle Logic (KBL) and its jointly digital and analogical codification of a KBL logophysics which surmounts the Cartesian divides.We introduce the nonorientable surfaces of selfreference, the Moebius strip and the Klein Bottle, as the metaform of morphogenesis, pattern formation and recognition, and its support of cognition and reality, and still as the metaform which connects through resonance, and the HyperKlein Bottles heterarchical superposition of KBs and a particular one which embodies a processual domain of semiosis, primally based on Feeling and the Peircian triad. We relate the KBL to the reentrance of the form in the Laws of Form of Spencer-Brown and the vortical torsion geometries of spacetime in quantum physics, condensed matter, liquid crystals, fluid-dynamics, the quantum foam structure of the vacuum and the fundamental interactions, which are processual, rather than simply containers of events, and still are fundamental to the Topological Chemistry paradigm. We further relate it to the fundamental cycles of Nature and thought –the latter as “strange loops” whose momentum is quantized, and the relation with spin and Planck constant, and discuss its extension to the subquantum domain. We further discuss their relation to asymmetry as non-commutativity of the product in decision theory, quantum mechanics at large, and still the Matrix Logic form of the KBL, where the True and False operators are not dual-commutative but embodied as the KB. We discuss the role of it with regards to Quantum Information Theory and the generation of transdual computation. We discuss Peirce’s triad and semiosis, in terms of the KBL and their hyperextension, starting with the topological non-orientable metaform of Feeling. We discuss the relation of the principle of selfreference in the construal and operation of language, and the higher-order forms of cognition, such as culture. We present a thorough discussion of the toroidal Topological Dynamics of Tozzi & Peters in the neurosciences, and its censorship of nonorientability and torsion geometry that was further proposes along the Fingelkurts et al hierarchical organization and operation of the brain, in complete disregard of the unified bodymind, and its non-orientable architecture already at a cellular level. We propose instead for the bodymind an iterated nonorientable organization and crossinteraction of octaves, and present several evidences for it, already at the tissue level and the electromagnetic fields supporting EEGs, the 𝞹- periodic selforganizing structure of the primal visual cortex and its KBL topology -which can also be conceived as the blowup of the origin as a singularity, the Moebius strip architecture of the mammal heart and that of the Anatomy Trains of the connective fascia system crucial to bodymind coherence, and the complex logarithm function of vision and dermatomal somatosensory organization of the body; this function at the level of spacetime introduces a torsion given by the logarithmic gradient of the wavefunction of quantum mechanics which is thus introjected as the visual system codification. In particular, we present a KBL representation of the Markov Blanket model for the inferential brain proposed by Friston and present the somatosensory and visual systems as their paramount examples. We present a panpsychism-panexperientalism of spacetime in terms of the Penrose’s twistor torsion fields given by the square root of the Null logical operator of Matrix Logic, produced by quaternionic light rays, and thus relate light to seeing and thinking, since the logophysical operators can be generated by the eigenstates supported by such quaternionic torsion light rays. We discuss the continuity of these structures as spacetime processes and that of the bodymind in terms of the Matrix Logic, which is given by the KBL torsion of cognitive space, and the fact that they support a quaternionic structure which thus appears as supporting the experience of light-seeing-thinking as if objective reality, and their supporting the geometry of spiral waves which are both proper to rotational spiral galaxies and the patterns appearing as vortical phosphenes in visual experience, and thus the fusion of objective reality and the structures of vision and thinking is realized concretely in terms of light rays with a quaternionic –non-commutative-structure as torsion geometries of either spacetime, the visual experience, or still of the supradual KBL of cognition. We discuss this as a realization of Max Velmans’ Reflective Monism, which also extends to the homology of the higher-order forms of cognition and social organization, as transpires from the phenomenological sociology due to Berger & Luckmann, and to the ethics proposed by Levinas. We present this homology between the domain of thought and cognition and that of spacetime structures to the theory of modelization proposed in psychology by Roger Shepard, both for music as spatial structures and to vision, in particular, and identify the non-orientable topology of this, as an introjection of the spacetime torsion geometry of dynamical particles with spin submitted to torsion fields. We discuss this in terms of JJ Gibson’s theory of the systemic nature of perception as an ecological psyche. In particular, the “mental” rotations identified by Shepard are found to be realized and pervasive to the anatomy-physiology of the brain, and particularly the dynamical systems approach to the neurosciences with the brain operating as a metastable chaotic system we reveal the non-orientable topologies of their chaotic attractors, were censored by Tozzi & Peters in their Topological toroidal neurosciences as a chaotic system. We discuss the crucial role of torsion and non-orientability as memory supporting, in extending along the basic lines of the Leyton’s extension to Shepard’s theory. We discuss the role of the nonorientability by transducing energy as resonant systems, which has been theoretical verified and empirically realized, and suggest its bearing in the resonant coherence of the brain as supporting a selfhood as a binding field, the 40Hz oscillation, and still crucial to the reduction of the quantum state in the antipodal identification of the quantum projective Hilbert space geometry of quantum mechanics. We suggest its role in the holographic form of the distribution of the energy of the trajectory of stars along their celestial motion, the Kozyrev effect which he associated to vortical torsion fields, in the resonant structures of pulsars and the Sun with a 160 minutes oscillation identified by Severny & Kotov, and still the palindromic Moebius strip structure of the histograms of seemingly random processes and their manifestation in terms of the periodic daily, monthly and sidereal cycles identified in the last sixty years by Simon Shnoll, and independently by Piccardi. We present a thorough elaboration of the non-orientable structure associated to projective geometry antipodal identification, inaugurated by the Renaissance Masters, as the geometry and topology which support selfawareness –in addition to the unconscious modeling as in Shepard’s Complementarity Principle in psychology previously introduced. Particularly, we discuss the latter with regards to the non-orientable topologies of the cognition of music and in particular, the four dimensional Clifford torus, and the Moebius strip surfaces edged by the periodic knots produced by this cognition, yet which supports the notion of elementary particles as Moebius strips thus produced, and their association with non-linear sine-Gordon solitons .We identify the topological metaform of selfhood, as pioneerly introduced by Heidegger and further elaborated by Malpas, Merleau-Ponty, Rosen, and Rapoport, as arising from the paradoxical embedding of the Klein Bottle in ambient space by selfpenetrating, as a higher form of embedding of the Moebius strip on 3d ambient space, and the KB unraveling in displaying the Klein Bottle in four or five dimensions which we have already proposed as the fundamental operation to support the harmonics of the brain connectome in producing both pattern formation and pattern recognition. All in all, the Klein Bottle appears as the metaform pattern which connects –as Bateson put its putative existence, morphs and creates. This is so for both the physical domain of reality and the structures and process of the bodymind, which by simply blowing up the origin as a singularity, a process already recognized in the paradigm of the brain as a visual producing “engine”, generates not only the world of reality, selfhood, the human bodyplan but the cosmos at large, which already starts in the non-orientable Moebius strip topology of the quantum foam vacuum, producing thus an alternative conception to the imperative makeshift Big Bang cosmology.